1. The Field of the Invention
The present invention pertains to a Hybrid One-way and Full-way (HOF) wave equation migration method for seismic imaging. With this HOF method, a one-way wave equation propagator is applied in extremely complicated geologic media with strong turning waves and duplex waves. For prestack depth migration, the source and receiver wavefields are extrapolated independently using the HOF propagator. A frequency-space domain imaging condition is applied at each frequency for one way extrapolation, while a time-space domain imaging condition is applied at each time slice for full-way extrapolation. An amplitude matching factor is introduced to form the final subsurface image from the one-way and full-way migrations. The HOF migration produces superior image quality over a one-way method. Compared with a full-way wave equation migration, the HOF migration significantly improves the computational efficiency, saves computational resources, and reduces the wavefield noise.
2. The Prior Art
In a frequency-space domain, a full-way wave equation can be decoupled into up-going and down-going wave equations. One-way wave equation migration methods, such as Finite-Difference (FD) scheme, Split Step Fourier (SSF), Fourier Finite Difference (FFD), Generalized Screen Propagator (GSP), and Local Cosine Beamlet (LCB) methods extrapolate down-going waves and are able to handle strong lateral velocity variations with great accuracy and efficiency Stoffa et. Al., (1990) propose an SSF method that was implemented in both frequency-space and frequency-wave number domains. SSF migration handles smoothly laterally varying velocity. Ristow and Rühl, (1994) proposed an FFD method wherein the downward continuation operator is split into two downward-continuation operators: one is a phase-shift operator for chosen constant background velocity, and the other is an optimized finite-difference operator for the arbitrary velocity function. FFD migration shows a better maximum dip-angle behavior than the SSF method. The dip limitation depends on the variation of the velocity field. Jin and Wu, (1998) proposed a windowed GSP method wherein the velocity field i9s partitioned into a few blocks in which the velocity perturbation is small. Within each block, a GSP migration is applied by using windowed Fourier transform. Luo and Wu (2003) proposed a LCB method that decomposes the wavefield into beamlets. Each beamlet propagates itself. The beamlets are coupled to each other after propagating to the next depth level. Small velocity perturbation within each beamlet and the orthogonal local cosine basis lead to the high accuracy and efficiency for the migration. Because of neglecting the up-going waves, all of these one-way methods don't take into account turning waves and duplex waves. Therefore, the one-way methods fail to reconstruct any vertical fault or salt overhang, as well as some subsalt events contributed from the overturned reflections and duplex waves.
To address the imaging problem encountered in one-way migration, the full-way wave equation, known as Reverse-Time Migration (RTM), extrapolates both down-going and up-going waves simultaneously. Baysal et al. (1983) proposed a RTM method by reverse extrapolation it time. No approximation is applied to the full-way wave equation. It can handle steeply dipping structures in a completely variable velocity medium. Baysal et al., (1984) further proposed a two-way non-reflecting wave equation to highly reduce the reflection coefficients for transmission across the material boundaries and interfaces. It can be useful when there's a need to avoid the strong interlayer reverberations. Whitmore, (1983) proposed an iterative depth migration by backward time prolongation. The migration is conducted in time domain with the time-reversed seismic section applied as upper surface boundary conditions. Chang and McMechan (1990) implemented a 3D common-shot prestack RTM using an excitation-time imaging condition for each imaging point in a 3D volume. Yoon et. Al. (2004) presented several challenges to remove artifacts in RTM migration and to increase the computational efficiency. In RTM migration, most wave modes that physically favor the wave propagation are correctly imaged if the geologic velocity model is true. Since there's no approximation to the full-way wave equation, RTM can image very steep dip and even vertical events. However, there are lots of technical issues that limit the practical application of RTM, such as numerical dispersion for high frequency wavefields, strong wavefield noise for a sharp boundary with strong velocity contrast, large disk space and large memory space required, and computationally expensive, etc. There are also many techniques proposed to deal with such issues, for example, choosing suitable Finite Difference schemes to improve the computation efficiency and taking less memory space, storing the useful wavefield with larger grid spacing may save disk space, cutting the model into several smaller pieces can save memory and disk space; and selecting properly designed imaging conditions can reduce the background noise. But even with these efforts, RTM is still a heavy burden for 3D seismic imaging.
In real earth models, the shallow geologic structures are usually simple, especially for seismic exploration in deep-water, such as in the Gulf of Mexico where the shallow portion is covered by water which has a constant velocity. In this case, one-way wave equation migration is good enough to produce a superior image. Since the shallow velocity is lower, it requires a finer grid spacing for full-way wave equation migration to reduce the effect caused by the numerical dispersion, thus dramatically increasing the computational cost. For salt dome structures, the velocity contrast is very strong between the sediment and salt body. Full-way migration usually generates strong wavefield noises caused by the grid diffractions at the sharp boundary. One-way migration produces a clean image with acceptable accuracy for imaging the shallow structures. However, the geologic structures are more complex in deep part, full-way migration is a better method to image complex structures. The present invention makes it possible to get high quality image for both shallow and deep parts of the whole model. The inventors propose a Hybrid One-way and Full-way (HOF) wave equation migration method by taking advantages from both one-way and full-way migration methods. One-way wave equation migration is conducted on the shallow part of the model, while full-way wave equation is conducted on the deep part of the model with complicated geologic structures in complex geologic medium where turning waves and duplex reflections have significant contributions.
There are two primary benefits for the subject HOF migration method. One is the improved image quality, better imaging in the shallow part of the geologic model with much less background noise and in the deep part with high accuracy. The other is greatly improving the computational efficiency and requiring less disk space and memory space, which are critical for 3-D seismic imaging.
In this disclosure, the inventors propose a Hybrid One-way and Full-way wave equation Migration method (HOF) for seismic imaging. The target oriented character and strategy are also disclosed for the migration with HOF.